An outbreak of an infectious illness can have a devastating impact on a population. Once confirmed, local health care organizations will attempt to reduce the spread of the disease by adopting a set of pre-defined guidelines. Modelling such a system presents a number of unique challenges: timing and probability constraints must be captured, scaling must be seamless and methods for analysis must be robust and efficient. To satisfy these requirements, an augmented form of Petri net known as a choice-point net is introduced in this thesis. In this data structure, timing is associated with event-based transitions that may fire multiple times to simulate the same event occurring several times in parallel. Events may result in several possible outcomes, or choices, each of which is given a probability of occurrence. A choice-point net may be scaled without requiring structural changes to the model and may be analyzed by unravelling it into a finite-state automaton representing (perhaps portions of) its behaviour. By translating questions about the protocol into the mathematical language of the net, recursive algorithms may then be employed to provide health-care professionals with answers to their questions. To demonstrate the expressiveness of choice-point nets, an actual, in-use protocol to control respiratory infection outbreaks in long-term care homes is modelled. Three similar abridged scenarios set in a small long-term care home are also modelled, analyzed and compared.